NEET Physics Question - Kinematics - Relative Motion in Two Dimension

A boy is running on a levelled road with velocity (v) with a long hollow tube in his hand. Water is falling vertically downwards with velocity (u). At what angle to the vertical, should he incline the tube so that the water drops enters without touching its side :

\[tan^{-1}\left( \frac{v}{u} \right)\]

\[sin^{-1}\left( \frac{v}{u} \right)\]

\[tan^{-1}\left( \frac{u}{v} \right)\]

\[cos^{-1}\left( \frac{v}{u} \right)\]

Solution:

The tube should be inclined at an angle \(\theta\) such that the water's relative velocity to the boy is along the axis of the tube.

The horizontal velocity of the boy is \(v\), and the vertical velocity of the falling water is \(u\). The angle \(\theta\) between the tube and the vertical satisfies:

\[
\tan \theta = \frac{v}{u}
\]

Thus, the required angle is:

\[
\theta = \tan^{-1} \left( \frac{v}{u} \right)
\]

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Solution:

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